Optimal model averaging for divergent-dimensional Poisson regressions

Predicting the multivariate zero‐inflated counts: A novel model averaging method under Pearson loss

“…Condition C3 presents some mild restrictions on the mean functions of the zero‐inflated Poisson and logit components, similar conditions can be found in Flynn et al, 45 Zou et al, 29 and Liu et al 30 ;…”

“…and (a) Condition C1 requires the n 1∕2 -consistency of estimators in misspecified models and White 44 provides a theoretical proof of this property under a compact subgroup with certain assumptions; (b) Condition C2 requires 𝜉 n to diverge at a speed no slower than n 1∕2 , implying a restriction on how close the candidate models can be to the true model and it also excludes any scenario where the true model(s) are included in the pool of candidate models. 45 This condition is similar to but weaker than Condition (7) of Ando and Li 46 and Condition (A3) of Ando and Li 47 ; (c) Condition C3 presents some mild restrictions on the mean functions of the zero-inflated Poisson and logit components, similar conditions can be found in Flynn et al, 45 Zou et al, 29 and Liu et al 30 ;…”

“…Remark (Some comments on Conditions C1‐C5) Condition C1 requires the $$$ {n}^{1/2} $$$‐consistency of estimators in misspecified models and White 44 provides a theoretical proof of this property under a compact subgroup with certain assumptions; Condition C2 requires $$$ {\xi}_n $$$ to diverge at a speed no slower than $$$ {n}^{1/2} $$$, implying a restriction on how close the candidate models can be to the true model and it also excludes any scenario where the true model(s) are included in the pool of candidate models 45 . This condition is similar to but weaker than Condition (7) of Ando and Li 46 and Condition (A3) of Ando and Li 47 ; Condition C3 presents some mild restrictions on the mean functions of the zero‐inflated Poisson and logit components, similar conditions can be found in Flynn et al, 45 Zou et al, 29 and Liu et al 30 ; Similar to Condition (15) of Zhu et al 31 and Condition 5 of Gao et al, 34 Condition C4 imposes certain boundedness on the largest singular value of $$$ \boldsymbol{\Sigma} $$$, $$$ {\boldsymbol{\Sigma}}^{\ast}\left(\boldsymbol{\pi} \right) $$$ and $$$ {\hat{\boldsymbol{\Sigma}}}^{-1}\left(\boldsymbol{\pi}, \mathbf{y}\right) $$$, as well as the convergence of the largest singular value of $$$ {\hat{\boldsymbol{\Sigma}}}^{-1}\l...$…”

“…As pointed out by one referee, there are several ways, in addition to the CV method, for optimal weight determination in practice, such as the Mallows criterion, 22,48,55 Kullback-Leibler criterion, 27,29,30,56 Jackknife or leave-one-out approach, 47,[57][58][59] and forward-validation technique. [60][61][62] Each method has its own merit and usage scenario.…”

“…Fortunately, such a dilemma can be well avoided by adopting the model averaging (MA) technique and various MA methods are discussed under different models and conditions, more details can be found in Hansen, 22 Liu and Okui, 23 Qiu et al, 24 Fang et al, 25 Li et al, 26 and so forth. To the best of our knowledge, there are a few MA techniques designed under univariate count model, [27][28][29][30] and a handful of works on MA estimation/predictions for multi-dimensional continuous data, [31][32][33][34] while relevant MA technique for multivariate count model has never been studied before. Therefore, we would like to provide a new MA prediction approach for multivariate count data analysis.…”